Cream butter; gradually add sugar, beating well. Add eggs, one at a time, beating well after each addition.
Combine flour, baking powder, and salt; add to creamed mixture alternately with milk, beginning and ending with flour mixture. Mix well after each addition. Stir in vanilla.
Pour batter into 3 greased and floured 9-inch round cake pans. Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes; remove layers from pans, and let cake cool completely.
Spread Rocky Mountain Filling between layers, and top with coconut.